## Speaker:

Peter Crooks

## Institution:

Northeastern University

## Time:

Monday, November 18, 2019 - 4:00pm

## Location:

RH 340P

Hessenberg varieties form a distinguished class of subvarieties in

the flag variety, and their study is central to themes at the interface of

combinatorics and geometric representation theory. Such themes include the

Stanley-Stembridge and Shareshian-Wachs conjectures, in which the cohomology

rings of Hessenberg varieties feature prominently.

I will provide a Lie-theoretic description of the cohomology rings of

regular Hessenberg varieties, emphasizing the role played by a certain

monodromy action and Deligne's local invariant cycle theorem. Our results

build on upon those of Brosnan-Chow, Abe-Harada-Horiguchi-Masuda, and

Abe-Horiguchi-Masuda-Murai-Sato. This represents joint work with Ana

Balibanu.